Major TV broadcasters petitioned the U.S. Supreme Court on Friday over Aereo Inc., a streaming-video startup backed by media mogul Barry Diller.

The broadcasters argue that Aereo, which streams local TV signals over the Web without their permission, violates their copyrights. The broadcasters, that include Walt Disney Co.'s ABC, Comcast Corp.'s NBC, CBS Corp. and 21st Century Fox, are appealing a ruling earlier this year by the U.S....